Abstract
The “mean speedup” of a trace monoid can be interpreted as an index of the “intrinsic parallelism”. We study the problem of computing the mean speedup under two conditions: (1) uniform distribution on the words of given length and (2) uniform distribution on the traces of given height. In the first case, we give an approximability result showing a probabilistic fully polynomial time approximation scheme, while, in the second case, we prove that the problem is NP-hard to approximate within n 1 − ε for every ε> 0, unless NP = coR.
This work is partially supported by the MIUR PRIN Project “Automata and Formal languages: mathematical and application driven studies”.
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Bertoni, A., Radicioni, R. (2007). Approximability and Non-approximability Results in Computing the Mean Speedup of Trace Monoids. In: Harju, T., Karhumäki, J., Lepistö, A. (eds) Developments in Language Theory. DLT 2007. Lecture Notes in Computer Science, vol 4588. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73208-2_10
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DOI: https://doi.org/10.1007/978-3-540-73208-2_10
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